Bochner's theorem and minimal foliation. (Théorème de Bochner et feuilletage minimal.)
Cartan connection of transversally Finsler foliation
The purpose of this paper is to define transversal Cartan connection of Finsler foliation and to prove its existence and uniqueness.
Cheeger-Chern-Simons classes of transversally symmetric foliations: Dependence relations and eta-invariants.
Classification de feuilletages totalement géodésiques de codimension un.
Codimension one foliations on complex tori
We prove a structure theorem for codimension one singular foliations on complex tori, from which we deduce some dynamical consequences.
Codimension one foliations without compact leaves.
Codimension one minimal foliations and the fundamental groups of leaves
Let be a transversely orientable transversely real-analytic codimension one minimal foliation of a paracompact manifold . We show that if the fundamental group of each leaf of is isomorphic to , then is without holonomy. We also show that if and the fundamental group of each leaf of is isomorphic to (), then is without holonomy.
Codimension one symplectic foliations.
We define the concept of symplectic foliation on a symplectic manifold and provide a method of constructing many examples, by using asymptotically holomorphic techniques.
Cohomologie basique et dualité des feuilletages riemanniens
Nous démontrons des théorèmes de dualité de Poincaré et de de Rham pour la cohomologie basique et l’homologie des courants transverses invariants d’un feuilletage riemannien.
Complétude des deux-tores lorentziens
Complétude et flots nul-géodésibles en géométrie lorentzienne
On étudie la complétude géodésique des flots nul-prégéodésiques sur les variétés lorentziennes compactes, ce qui donne une obstruction à être nul-géodésique. On montre que lorsque l’orthogonal du champ de vecteurs engendrant le flot considéré s’intègre en un feuilletage , la complétude du flot se lit sur l’holonomie de . On montre ainsi qu’il n’existe pas de flots nul-géodésiques lisses sur . On montre aussi qu’un -tore lorentzien est nul-complet si et seulement si ses feuilletages de type lumière...
Constancy of maps into -manifolds and pseudo -manifolds.
Controlled constructions of Reeb fields and applications. (Constructions contrôlées de champs de Reeb et applications.)
Correspondence between diffeomorphism groups and singular foliations
It is well-known that any isotopically connected diffeomorphism group G of a manifold determines a unique singular foliation . A one-to-one correspondence between the class of singular foliations and a subclass of diffeomorphism groups is established. As an illustration of this correspondence it is shown that the commutator subgroup [G,G] of an isotopically connected, factorizable and non-fixing diffeomorphism group G is simple iff the foliation defined by [G,G] admits no proper minimal sets....
Cosymplectic and α-cosymplectic Lie algebras
Courbure totale des feuilletages des surfaces.
De Rham Decomposition of Affinely connected manifolds.
De Rham decomposition theorems for foliated manifolds
We prove that if is a complete simply connected Riemannian manifold and is a totally geodesic foliation of with integrable normal bundle, then is topologically a product and the two foliations are the product foliations. We also prove a decomposition theorem for Riemannian foliations and a structure theorem for Riemannian foliations with recurrent curvature.
De Rham-Hodge Theory for Riemannian Foliations.
Decomposition theorems in differential geometry.